Speaker
Description
We investigate the inclusive and semi-inclusive productions of spin-3/2 hadrons, such as $\Omega$, in unpolarized $e^+e^-$ annihilation and lepton-nucleon deep inelastic scattering. The quark transverse momentum dependent (TMD) fragmentation functions (FFs) to spin-3/2 hadrons are defined for the first time from the decomposition of the quark-quark correlator at leading twist, 14 of which are newly defined for rank-3 tensor polarized hadron states. We perform a leading order calculation of the differential cross sections. In the inclusive hadron production in $e^+ e^-$ annihilation, only two structure functions are found nonzero and none of the rank-3 tensor polarized FFs contributes. For two-hadron production, half of the 48 structure functions are found nonzero even if the spin of the second hadron is not analyzed, and ten of the rank-3 tensor polarized TMD FFs contribute. These newly defined FFs can be further applied in semi-inclusive deep inelastic scattering (SIDIS) processes for the study of nucleon structures. For completeness, we consider the situations where all particles are polarized in SIDIS. For the unpolarized lepton case, half of 192 structure functions are nonzero and 42 of rank-3 tensor polarized TMD FFs contribute. Furthermore, if we consider the polarized lepton, one-third of 96 structure functions are nonzero and 14 of the nonzero structure functions are for rank-3 tensor polarized hadron states.
